Boris Johnson has rejected the suggestion from Nigel Farage and Donald Trump that he should work with the Brexit Party during the election.
The Tory leader told the BBC he was “always grateful for advice” but he would not enter into election pacts.
His comments come after the US president said Mr Farage and Mr Johnson would be “an unstoppable force”.
Downing Street sources say there are no circumstances in which the Tories would work with the Brexit Party.
In an interview with BBC political editor Laura Kuenssberg, the prime minister said the “difficulty” of doing deals with “any other party” was that it “simply risks putting Jeremy Corbyn into Number 10”.
“The problem with that is that his [Mr Corbyn’s] plan for Brexit is basically yet more dither and delay,” Mr Johnson said.
Mr Johnson also said there was “no question of negotiating on the NHS” as part of any future trade deal with the US, but he did not rule out expanding the amount of private provision in the health service in the future.
But Labour’s shadow health secretary, Jonathan Ashworth, said the public “can’t trust the Tories on the NHS”, saying they would “increase privatisation even further and do a deal with Donald Trump”.
When pushed on whether he would rule out a deal with Mr Farage, Mr Johnson replied: “I want to be very, very clear that voting for any other party than this government, this Conservative government… is basically tantamount to putting Jeremy Corbyn in.”
The UK is going to the polls on 12 December following a further delay to the UK’s departure from the EU, to 31 January 2020.
The BBC will be talking to other party leaders during the course of the campaign.
US president Donald Trump told Nigel Farage’s LBC show on Thursday that the Brexit Party leader should team up with Mr Johnson to do “something terrific” and he also criticised the prime minister’s EU withdrawal agreement.
Meanwhile, Mr Farage has called on the prime minister to drop his Brexit deal, unite in a “Leave alliance” or face a Brexit Party candidate in every seat in the election.
Mr Johnson said there were “lots of reasons” why he thought a Labour government would be a “disaster”.
He said he Labour government would lead to a renegotiation with Brussels on a Brexit deal, then another referendum.
“Why go through that nightmare again?” he said.
The prime minister also suggested that the US president was wrong to believe a trade deal would be impossible with the UK after Brexit.
Mr Johnson said his “proper Brexit” deal “enables us to do proper all-singing, all-dancing free-trade deals”.
“It delivers exactly what we wanted, what I wanted, when I campaigned in 2016 to come out the European Union,” Mr Johnson said.
When asked about the criticism from Mr Trump, Mr Johnson said: “I am always grateful for advice from wherever it comes and we have great relations as you know with the US and many many other countries.
“But on the technicalities of the deal anybody who looks at it can see that the UK has full control.”
The prime minister is never short of a word or two, never short of a colourful phrase or a metaphor.
When we sat down this afternoon there was no suggestion of him being the Hulk, but Remain-tending MPs were accused of “rope-a-doping” the government, planning eventually to batter the prime minister and his Brexit deal into submission until he would have had to give up.
But in Downing Street there is a serious awareness that trademark Johnson verbal gymnastics are no guarantee of success at the ballot box in six weeks’ time, no guarantee at all.
That’s not just because there are even friends, like Donald Trump, and of course foes, like Jeremy Corbyn, whose words and actions will hamper his attempt to secure a majority to call his own.
But also because this is a snap election, not a routine poll, and the public is hardly in a forgiving mood of our politicians right now.
Mr Johnson said he hoped the government could get Brexit “over the line” by the middle of January if he won a majority, claiming the current Parliament would never have passed his deal.
He said he’d had “no choice” but to call a general election, saying: “Nobody wants an election but we’ve got to do it now.
“This is a Parliament that is basically full of MPs who voted Remain.
“They voted Remain and they will continue to block Brexit if they’re given the chance – we need a new mandate, we need to refresh our Parliament.”
Mr Johnson said his government was determined to increase taxpayer funding of the NHS but said: “Of course there are dentists and optometrists and so on who are providers to the NHS, of course, that’s how it works,” he said.
“But… I believe passionately in an NHS free at the point of use for everybody in this country.”
Labour’s Mr Ashworth said: “Forced NHS privatisation has doubled under the Conservatives and Boris Johnson has refused to rule out expanding this further.
“You can’t trust the Tories on the NHS. They will increase privatisation even further and do a deal with Donald Trump that will see as much as £500m more a week sent to US corporations.”